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Models of Sleep and Alertness Dynamics

This document provides a basic description of the functionality of the Sydney-CRC Model of Alertness. It is intended to provide an overview of concepts and terminology of these models.

Overview

The Sydney-CRC Model of Alertness, hereafter referred to as the model, is a mathematical model that captures the biological dynamics underlying the sleep-wake cycle, circadian rhythms, and alertness in humans. That is, the model captures the dynamics of the build-up of a need for sleep with time spent awake, the recovery that occurs during sleep, and the associated effects on alertness and interactions with circadian rhythms. The model’s default configuration is based on comparisons with data collected both in the laboratory and in “real-world” situations. In this configuration its predictions correspond to the biological dynamics of an average or typical person. When evaluated without any additional constraints, the model will predict saturated sleep duration of 8.5 h per night starting at 23:30. These predictions of sleep are based on the times when the biological need for sleep exceeds a certain threshold.

It is important to note that the model does not, intrinsically, capture the behavioural decisions that result from work, social or environmental conditions. Just like for a person, these factors constrain the evolution of sleep-wake and alertness dynamics. For the model to make predictions that match “real world” behaviour of a specific person it is necessary to evaluate it in the context experienced by that person. This is achieved by providing inputs that capture the context in which the model should be evaluated. The contextual inputs that are currently supported take two main forms:

  • forced-wake; and
  • specific light exposure.

For example, for a given shift-schedule and commute times (time intervals of forced-wake) the model can be used to predict potential disturbances to sleep patterns and the effect on alertness.

By default the predicted dynamics correspond to those for a typical person, or equivalently a group average, in response to a specific context. However, further individualisation of the model’s predictions can be achieved by modifying the parameters that determine intrinsic dynamics – that is by modifying the model for inter-individual biophysical differences. For example, reducing the average daily sleep requirements of the model to make more accurate predictions for a person who only requires, say, an average of 6 hours sleep per night. NOTE: requires here means biological need – only getting 6 hours per night, due to behavioural, social, or environmental context, corresponds to an evaluation constraint, not an intrinsic property of the model’s dynamics.

The core of the model is a prediction of the dynamics of biological processes underlying the sleep/wake cycle and alertness. However, a range of mechanisms are in place for computing measures derived from this information and for summarising results.

The model’s functionality can be thought of as consisting of four main components:

The following sections outline these components in a bit more detail. This document then ends with a section outlining potential ways of making use of the model’s features and a final section providing references to some of the scientific publications describing and using the model.

Dynamics

The biophysical dynamics captured by the model is described by a set of coupled differential equations (see Further Reading for details). These equations define the temporal evolution of a set of variables (properties that vary with time, outlined below), with each variable representing a key biophysical process underlying the sleep/wake cycle. While the general properties of the dynamics are set by the form of the equations, the details can be adjusted using the equations’ parameters (properties intrinsic to the system, outlined below). For example, parameters can be used to adjust things like the average daily need for sleep.

It should be noted that the alertness-models code actually implements a set of closely related models, all having the same approximate form but each capturing slightly different sets of relevant biological processes underlying the human sleep-wake cycle. However, as we are only describing things at a conceptual level here, we will continue as though they are one thing. Also, here we are only describing the Sydney group’s models of Alertness, but a range of models from the literature are also implemented for reference.

A schematic of the main components of our sleep-wake and alertness dynamics models.

Variables

The main dynamic variables of the model capture four key biophysical components underlying the sleep/wake cycle, and how they change with time. Namely:

  • Mean Voltages of Neuronal Populations (eg VLPO and SCN, see Further Reading);
  • Homoeostatic Drive;
  • Circadian Clock; and
  • Photoreceptor activity.

The expressions defining the dynamics of each of these variables further encompasses the following set of supporting concepts:

  • Mean firing rate of neuronal populations;
  • Wake Effort;
  • Total Sleep Drive;
  • Circadian Drive, which can be further separated into photic and non-photic components; and
  • Sleep/Wake state, a threshold function operating on predictions of neuronal activity.

Parameters

The parameters of the model are used to control details of the dynamics. The default parameter values have been set based on comparisons between the model’s predictions and data collected in laboratory and “real-world” settings. These defaults can be thought of as capturing the sleep/wake dynamics of a typical person, and should be sufficient for a range of use-cases. However, when individualisation is required, tuning the sleep/wake and alertness predictions for an individual, the model’s parameters need to be adjusted. Such adjustment could either involve making direct modifications of specific parameters, or selecting from a set of predefined parameters corresponding to particular sleep/wake profiles.

There are a large number of parameters in the model, but most of them represent biophysical properties that do not vary greatly between individuals. The parameters that are good candidates for adjustment when individualising the model’s dynamics correspond to a few main concepts:

  • Rate of build-up in need for sleep (adjusts duration of wake period from a fully rested state);
  • Rate of recovery when asleep (adjusts duration of average required daily sleep);
  • Circadian Clock (adjusts alignment with clock-time); and
  • Sensitivity to light (adjusts the strength of effects deriving from light exposure).

Context

Whether in its default configuration or individualised, in the absence of a specific context for the evaluation, the model will provide relatively simple, periodic, predictions. To make predictions that are more relevant to real-world contexts, the model must be provided with input describing the constraints. These external constraints take two forms: forced-wake; and light exposure.

Forced-wake constraints can be introduced by two, alternative, mechanisms:

  1. directly (forced-wake), that is, by specifying any times when sleep is not possible; or
  2. inversely (sleep-opportunity), that is, by specifying all times for the duration of interest when sleep is possible.

The direct case involves providing inputs that represent things like work commitments. For example, shift times and durations of commute to and from a place of work can be provided as input to represent forced-wake (ie, “no sleep during this time”) constraints on the evaluation of the model. Alternatively, sleep-opportunities can be provided as inputs. Representing, for example, something like time-in-bed. Sleep-opportunities are just the inverse of forced-wake and internally are implemented as forced-wake at all times that are not explicitly specified as sleep-opportunities. It is important to note that, if provided, sleep-opportunities take precedence. That is, once you have specified at least one sleep-opportunity you must specify all time periods when the model should be allowed to fall asleep. As a practical consideration, unless there is a very strong reason to do otherwise, it is simpler to restrict inputs to be only in terms of direct forced-wake.

In the case of light-exposure, if no inputs are used then a typical day-night profile is applied. However, if specific light exposure is known, for example light levels in the work-place, then the light level can be specified for those time periods, replacing the generic day-night profile during that time.

Predictions

The core model predictions are generated from a combination of the model’s biophysical dynamics and the behavioural and environmental context, provided as input and constraints it imposes on the model’s evaluation.

As such, the core model predictions correspond to the continuous dynamics of the model’s variables, which were outlined above. These variable are typically evaluated at a one minute resolution for the duration of interest. That is, over one thousand measurements of each variable are generated per modelled day. For example, a core model prediction is a minute by minute prediction for the sleep/wake state of the model.

Output

The core model predictions serve as a basis for the output returned from the evaluation of the model. However, these direct results are often more detailed (continuous dynamics: many thousands of data points per day of predictions) and of a lower level (predictions being of underlying biophysical processes, not the behavioural responses they cause) than is required by most use-cases.

To address this, a range of mechanisms are in place to support summarising the information as well as converting it to derived measures that have validated functional relationships to core model variables.

The available derived measures fall into three main categories: sleep; alertness; and circadian. Specifically, the following measures are available:

  • Sleep:
    • Start and end time – sleep-predictions are based on the time periods corresponding to maximum biological need for sleep;
    • Duration;
  • Alertness:
    • Performance on Psychomotor Vigilance Task (PVT), response-times and lapses;
    • Karolinska Sleepiness Scale (KSS);
  • Circadian:
    • Core Body Temperature (CBT) minimum;
    • Melatonin:
      • Synthesis;
      • Dim Light Melatonin Onset (DLMO);
      • Plasma;
      • Saliva;
      • Urine, aMT6s acrophase.

And for each of these measures the values can be summarised, where applicable, by only returning:

  • Averages, for example:
    • hourly
    • during shift
    • during commute
  • Maximums and/or minimums, for example:
    • per day
    • per time-period, eg shift
  • Values at specific times, for example:
    • midnight each day;
    • start of shift;
    • end of shift
  • Phase alignment, for periodic measures.

In addition to the numeric data, image files containing basic visual depictions of the data, eg raster plots, can be returned.

By using the the model’s predictions it is possible to generate Sleep Recommendations, where information from the model’s predictions are used as a basis for making biophysically sensible sleep recommendations.

Generally, the point of making sleep recommendations is to improve or optimise some objective. As the model’s two main predictions are sleep and alertness these are the obvious objectives of optimisation.

Use-Cases

This section describes some generic use-cases, or potential uses of the model. At a very general level, there are three main purposes for wanting to evaluate the model:

  • a single evaluation of the model to make predictions under a specific context;
  • multiple evaluations of the model under differing contexts to identify an optimal outcome;
  • multiple evaluations of the model in differing configurations under a set of constraints with known responses (data source, such as actigraphy or alertness measures) – with comparison between predictions and known responses used to identify a (biophysically) individualised model configuration.

Some general examples would be:

  • Predictions for Group (Typical Person) Response to a Specific Schedule This is the simplest use-case. A single schedule (shifts, commutes, etc), covering a specific time period (eg. a few days or a week), is provided as input and the model is evaluated in its default configuration. A selection of measures are returned summarising the model’s predictions for sleep, alertness, and circadian information during the period of time for which the model is being evaluated, with details of what is returned depending on the specific use-case;
  • Predictions for Group (Typical Person) Response to a Range of Schedules This just corresponds to evaluating the model a number of times, once for each specific schedule;
  • Learning Model Configuration for a Specific Person The learning process is not part of the model. This case corresponds to the client being a machine-learning algorithm (or similar). For example, if sleep information is known for an individual on a specific schedule then, the model can be evaluated on that schedule in a range of configurations. The model’s predictions would then be compared to the known sleep pattern. This process can be repeated until an acceptable correspondence is obtained between the model’s predictions and the known sleep of the individual;
  • Predictions for a Specific Person on a Specific Schedule This is very similar to the Typical Person case, with the exception that modifications to the model’s default configuration are also provided, in addition to the schedule constraints, as input. This could take the form of selecting a predefined set of parameters that correspond to some general properties of the model’s dynamics that more closely fit an individual, for example, having shorter or longer duration of average daily sleep requirement than a typical person. Or it could be detailed individualised parameters that have been learnt by adapting the model’s configuration to known sleep patterns of an individual;
  • Recommendations for a Group (Typical Person) on a Specific Schedule The model does not make recommendations, however it does provide the necessary information to serve as the basis of sensible recommendations. The two main potential forms of recommendation would be sleep recommendations or light exposure recommendations. In both cases, one approach would be to perform repeated evaluations of the model for a range of constraints, selecting the constraints that optimises the model output of interest (eg. amount of sleep, alertness during some time period, circadian alignment to a schedule or time-zone change), and providing that as the recommendation;
  • Recommendations for a Specific Person on a Specific Schedule This is effectively just a combination of the “Predictions for a Specific Person on a Specific Schedule” case and the “Recommendations for a Group (Typical Person) on a Specific Schedule” case.